Pablo Navarrete

We demonstrate that at finite density and sufficiently high temperatures, phase-quenched (PQ) lattice simulations combined with perturbation theory provide a new precision approach to determining the thermodynamics of QCD across a wide arc of the phase diagram where the strong coupling constant α s remains small. In this regime, nonperturbative pairing effects in the PQ theory are parametrically suppressed, so that the difference between the PQ and full QCD pressures becomes a small perturbative correction. We compute this correction up to and including O ( α s 7 / 2 ) using electrostatic QCD together with a novel numerical method to compute four-loop sum-integrals. This enables the determination of the perturbative QCD pressure with precision beyond the current state of the art while including nonperturbative pure-gluonic contributions from the lattice.

A bstract: We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the limitations of standard high-temperature approximations. By systematically disentangling the physics of hard and soft momentum scales, our approach unifies their treatment within a single expression, enabling consistent handling of both vacuum and thermal divergences across all mass regimes. This core innovation enables the efficient numerical evaluation of massive multiloop thermal sum-integrals, achieved through a finite-temperature generalization of Loop-Tree Duality — an advanced algorithmic technique originally developed to render vacuum Feynman integrals numerically tractable via Monte Carlo methods. As a proof of principle, we apply the framework to a scalar-Yukawa model, presenting a complete two-loop calculation and a novel three-loop extension — the first fully massive three-loop sum-integral computation without relying on high-temperature expansions. Our approach opens the door to precise perturbative predictions of the phase structure in a broad class of beyond-the-Standard-Model scenarios, including those featuring strong first-order phase transitions relevant for gravitational-wave signals, where conventional high-temperature approximations break down.

We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the limitations of standard high-temperature approximations. By systematically disentangling the physics of hard and soft momentum scales, our approach unifies their treatment within a single expression, enabling consistent handling of both vacuum and thermal divergences across all mass regimes. This core innovation enables the efficient numerical evaluation of massive multiloop thermal sum-integrals, achieved through a finite-temperature generalization of Loop-Tree Duality -- an advanced algorithmic technique originally developed to render vacuum Feynman integrals numerically tractable via Monte Carlo methods. As a proof of principle, we apply the framework to a scalar-Yukawa model, presenting a complete two-loop calculation and a novel three-loop extension -- the first fully massive three-loop sum-integral computation without relying on high-temperature expansions. Our approach opens the door to precise perturbative predictions of the phase structure in a broad class of beyond-the-Standard-Model scenarios, including those featuring strong first-order phase transitions relevant for gravitational-wave signals, where conventional high-temperature approximations break down.

Knowledge of the pressure of cold and dense quark matter is known to significantly constrain the equation of state of neutron-star matter, a quantity playing a key role in deciphering the stars’ internal structure. In this Letter, we make important progress toward determining the last unknown contribution to the pressure at next-to-next-to-next-to-leading order in the strong coupling constant α s , available through the sum of all four-loop vacuum diagrams of dense quantum chromodynamics. We demonstrate the cancellation of both the covariant gauge parameter and all infrared divergences in the sum, showcasing the effective-field-theory paradigm in action. For the remaining infrared-finite four-loop integrals, we demonstrate the efficacy of the dense loop tree duality method—a novel numerical framework for multiloop calculations in thermal field theory. Together, our results show that completing the next-to-next-to-next-to-leading order pressure of cold quark matter is no longer merely possible but for the first time within reach.

Nonperturbative inequalities constrain the thermodynamic pressure of quantum chromodynamics (QCD) with its phase-quenched version, a sign-problem-free theory amenable to lattice treatment. In the perturbative regime with a small QCD coupling constant α s , one of these inequalities manifests as an O ( α s 3 ) difference between the phase-quenched and QCD pressures at large baryon chemical potential. In this work, we generalize state-of-the-art algorithmic techniques used in collider physics to address large-scale multiloop computations at finite chemical potential, by direct numerical integration of Feynman diagrams in momentum space. Using this novel approach, we evaluate this O ( α s 3 ) difference and show that it is a gauge-independent and small positive number compared to the known perturbative coefficients at this order. This implies that at high baryon densities, phase-quenched lattice simulations can provide a complementary nonperturbative method for accurately determining the pressure of cold quark matter at O ( α s 3 ) . Published by the American Physical Society 2024

We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the result onto one-loop structures, thereby proving factorization also in the sum-integral setting. Analytic results are provided for generic integer-valued propagator- and numerator-powers of the class of sum-integrals under consideration, allowing to eliminate them from any perturbative expansion, dramatically simplifying the evaluation of some observables encountered e.g. in hot QCD.